In recent years, a travel assist apparatus which controls travel of a vehicle according to a set target has been under development. As one example of such a travel assist apparatus, there is known an apparatus that performs vehicle control such that the distance between two vehicles, that is, a host vehicle and a preceding vehicle present ahead of the host vehicle in the traveling direction of the host vehicle, is kept at a predetermined distance or more (refer to Patent Document 1, for example).
In the above-described apparatus, the distance between the host vehicle and the preceding vehicle is monitored. Then, when the distance between the two vehicles is less than a predetermined distance, a difference is calculated by subtracting the distance between the two vehicles from the predetermined distance, thereby controlling the vehicle speed (more specifically, a relative speed of the host vehicle with reference to the preceding vehicle) such that the difference becomes less than 0 (zero). For example, a target relative deceleration is set to be a greater value when the above-described difference is great than when the difference is small. Speed-reduction control is performed such that a relative deceleration of the host vehicle with reference to the preceding vehicle is brought close to the target relative deceleration.